To enable scalable probabilistic inference, it is essential to represent three different types of independencies in the modeling language. Firstly, the traditional classical conditional independencies (CIs) represented by Bayesian networks (BNs). Secondly, the context-specific independencies (CSIs): independencies that hold only in certain contexts [1]}. These independencies arise due to structures present in conditional probability distributions (CPDs) of BNs, which BNs do not qualitatively represent, but rule-based representations do by making structures explicit in the clauses [2]}.
Thirdly, the combining rules such as NoisyOR to express probabilistic influences among attributes of related objects [3]}, [4]}. Combining rules are particularly interesting since they allow one to qualitatively represent independence of causal influences [5]}, where each influence is considered independent of others. This independence is natural and commonly assumed to keep relational models succinct [6]}. In probabilistic logic programs that deal with only discrete random variables, combining rules are the core component [7]}, [8]}.
